Pertanyaan

Bentuk rasional dari 5 + 15 6 − 3 adalah ....

Bentuk rasional dari $\frac{6 - 3}{5 + 15}$ adalah ....

$begin mathsize 14px style fraction numerator 5 square root of 5 plus 3 square root of 6 minus square root of 10 minus 3 square root of 15 over denominator 10 end fraction end style$
$begin mathsize 14px style fraction numerator 3 square root of 5 plus 5 square root of 6 minus 3 square root of 10 minus square root of 15 over denominator 10 end fraction end style$
$begin mathsize 14px style fraction numerator 5 square root of 5 plus 3 square root of 6 minus 5 square root of 3 minus 3 square root of 10 over denominator 10 end fraction end style$
$begin mathsize 14px style fraction numerator 3 square root of 5 plus 5 square root of 6 minus 5 square root of 3 minus 3 square root of 10 over denominator 10 end fraction end style$

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan bahwa Jadi, bentuk rasional dari adalah . Dengan demikian, jawaban yang tepat adalah D.

Perhatikan bahwa

$begin mathsize 12px style fraction numerator square root of 6 minus square root of 3 over denominator 5 plus square root of 15 end fraction equals blank fraction numerator square root of 6 minus square root of 3 over denominator 5 plus square root of 15 end fraction cross times fraction numerator 5 minus square root of 15 over denominator 5 minus square root of 15 end fraction equals fraction numerator open parentheses square root of 6 cross times 5 close parentheses minus open parentheses square root of 3 cross times 5 close parentheses minus open parentheses square root of 6 cross times square root of 15 close parentheses plus left parenthesis square root of 3 cross times square root of 15 right parenthesis over denominator 5 squared minus open parentheses square root of 15 close parentheses squared end fraction equals fraction numerator 5 square root of 6 minus 5 square root of 3 minus square root of 90 plus square root of 45 over denominator 25 minus 15 end fraction equals fraction numerator 5 square root of 6 minus 5 square root of 3 minus square root of 9 cross times 10 end root plus square root of 9 cross times 5 end root over denominator 10 end fraction equals fraction numerator 5 square root of 6 minus 5 square root of 3 minus 3 square root of 10 plus 3 square root of 5 over denominator 10 end fraction equals fraction numerator 3 square root of 5 plus 5 square root of 6 minus 5 square root of 3 minus 3 square root of 10 over denominator 10 end fraction end style$

Jadi, bentuk rasional dari $begin mathsize 14px style fraction numerator square root of 6 minus square root of 3 over denominator 5 plus square root of 15 end fraction end style$ adalah .

Dengan demikian, jawaban yang tepat adalah D.